The combination of surface chemistry and roughness' on the micron and nanoscale imbues enhanced repellency to the lotus leaf surface when in contact with a high surface tension liquid such as water (surface tension g = 72.1 mN/m). This understanding has led to the creation of a number of artificial superhydrophobic surfaces (water contact angles greater than 150°, low hysteresis). However, researchers so far have been unsuccessful in producing super-oleophobic surfaces for liquids with much lower surface tensions; for example alkanes such as decane (g = 23.8 mN/m) or octane (g = 21.6 mN/m). Theoretical calculations suggest that a super-oleophobic surface would need to have a surface energy < 5 mN/m, whereas the lowest solid surface energies reported to date are in the range of ~6 mN/m. In this work, we explain how a third factor, surface curvature (apart from surface chemistry and roughness), can be used to significantly enhance liquid repellency, by studying electrospun polymer fibers containing very low surface energy perfluorinated nanoparticles (FluoroPOSS). Increasing the POSS concentration in the elecrospun fibers allows us to systematically transcend from super-hydrophilic to super-hydrophobic and finally to the first ever super-oleophobic surfaces (exhibiting low hysteresis and contact angles with decane and octane greater than 150°).